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We present classes of models in which particles are dropped on an arbitrary fixed finite connected graph, obeying adhesion rules with screening. We prove that there is an invariant distribution for the resulting height profile, and Gaussian concentration for functions depending on the paths of the profiles. As a corollary we obtain a law of large numbers for the maximum height. This describes the asymptotic speed with which the maximal height increases. The results incorporate the case of independent particle droppings but extend to droppings according to a driving Markov chain, and to droppings with possible deposition below the top layer up to a fixed finite depth, obeying a non-nullness condition for the screening rule. The proof is based on an analysis of the Markov chain on height-profiles using coupling methods. We construct a finite communicating set of configurations of profiles to which the chain keeps returning.
In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundar
We study the Fleming-Viot particle process formed by N interacting continuous-time asymmetric random walks on the cycle graph, with uniform killing. We show that this model has a remarkable exact solvability, despite the fact that it is non-reversibl
This paper is concerned with symmetric $1$-dependent colorings of the $d$-ray star graph $mathscr{S}^d$ for each $d ge 2$. We compute the critical point of the $1$-dependent hard-core processes on $mathscr{S}^d$, which gives a lower bound for the num
In this paper, we consider graphon particle systems with heterogeneous mean-field type interactions and the associated finite particle approximations. Under suitable growth (resp. convexity) assumptions, we obtain uniform-in-time concentration estima
Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing Gaussian laws may produce a potential with multiple deep wells. We study in the present work fi